Transport Equation and Tomography

Main designations
Introduction
Direct and inverse problems for the transport equation with energy dependence
Derivation of the radiation transport equation
Formulation and investigation of the direct problem for the transport equation
Continuity of solutions to the direct problem
Determination of the total attenuation coefficient for discontinuous density of the input flux
Description of a source with discontinuous radiation density
A boundary value problem with a parameter for the transport equation
Determining the total interaction coefficient by multiple irradiation
Providing special boundary conditions for multiple irradiation
Testing the algorithms for determining unknown media
The tomography problem in the monoenergetic case
The direct problem for the monoenergetic transport equation
Additional restrictions
A formula for the gradient of a solution to the transport equation
Auxiliary statements
The indicator of heterogeneity in the tomography problem, and the measure of visibility
Invisibility media in tomography
Computerized testing of the indicator of heterogeneity
Some contradictions between two mathematical models of transport theory
Comparing two models in transport theory in the plane-parallel case
Prospective investigation
Bibliography